Method of constructing and training a neural network

ABSTRACT

A method of processing a radio frequency signal includes: receiving the radio frequency signal at an antenna of a receiver device; processing, by a radio frequency front-end device, the radio frequency signal; converting, by an analog-to-digital converter, the analog signal to a digital signal; receiving, by a neural network, the digital signal; and processing, by the neural network, the digital signal to produce an output.

FIELD

The present disclosure relates to processing a radio frequency signalwith a receiver device including a trained neural network.

BACKGROUND INFORMATION

Existing wireless receivers suffer from interoperability problems. Oftenit is desirable for multiple radios built by different vendors and usingdifferent physical and access control radio technologies tointeroperate, but it is complicated for any single radio to host all theprocessing required to process all other waveforms.

A paper entitled “An Introduction to Deep Learning for the PhysicalLayer,” Jul. 11, 2017, Cornell University Library, arXiv:1702.00832v2,pages 1-13, by O'shea et al. describes several applications of deeplearning for the physical layer. This paper also describes that radiotransformer networks can be a means to incorporate expert domainknowledge in a machine learning (ML) model. It further describes theapplication or convolutional neural networks on raw IQ samples formodulation classification.

A paper entitled “Learning to Communicate: Channel Auto-encoders, DomainSpecific Regularizers, and Attention,” Aug. 23, 2016, Cornell UniversityLibrary, arXiv:1608.06409v1, pages 1-10, by O'shea et al. describesreconstruction optimization through impairment layers in a channelautoencoder and several domain-specific regularizing layers to emulatecommon channel impairments.

A paper entitled “Radio Transformer Networks: Attention Models forLearning to Synchronize in Wireless Systems,” May 3, 2016, CornellUniversity Library, arXiv:1605.00716v1, pages 1-5, by O'shea et al.describes introducing learned attention models into the radio machinelearning domain for the task of modulation recognition by leveragingspatial transformer networks and introducing new radio domainappropriate transformations. This attention model allows the network tolearn a localization network capable of synchronizing and normalizing aradio signal blindly with zero knowledge of the signal's structure basedon optimization of the network for classification accuracy, sparserepresentation, and regularization.

A paper entitled “Convolutional Radio Modulation Recognition Networks,”Feb. 12, 2016, Cornell University Library, arXiv:1602.04105v3, pages1-15, by O'shea et al. describes the adaptation of convolutional neuralnetworks to the complex-valued temporal radio signal domain.

A paper entitled “Unsupervised Representation Learning of StructuredRadio Communication Signals,” Apr. 24, 2016, Cornell University Library,arXiv:1604.07078v1, pages 1-5, by O'shea et al. describes unsupervisedrepresentation learning of radio communication signals in raw sampledtime series representation.

A paper entitled “Deep Architectures of Modulation Recognition,” Mar.27, 2017, Cornell University Library, arXiv:1703.09197v1, pages 1-7, byWest et al. describes applying machine learning with deep neuralnetworks to the task of radio modulation recognition.

A paper entitled “Semi-Supervised Radio Signal Identification,” Jan. 17,2017, Cornell University Library, arXiv:1611.00303v2, pages 1-6, byO'Shea et al. describes that semi-supervised learning techniques can beused to scale learning beyond supervised datasets, allowing fordiscerning and recalling new radio signals by using sparse signalrepresentations based on both unsupervised and supervised methods fornonlinear feature learning and clustering methods.

A paper entitled “Radio Machine Learning Dataset Generation with GNURadio,” Proceedings of the GNU Radio Conference, v. 1, n. 1, September2016, pages 1-6, by O'Shea et al. describes emerging applications of MLto the Radio Signal Processing domain.

A paper entitled “Deep Learning Based MIMO Communications,” Jul. 25,2017, Cornell University Library, arXiv:1707.07980v1, pages 1-9, byO'Shea et al. describes a physical layer scheme for single userMultiple-Input Multiple-Output (MIMO) communications based onunsupervised deep learning using an autoencoder.

SUMMARY

An exemplary embodiment of the present disclosure provides a method ofprocessing a radio frequency signal. The method includes: receiving theradio frequency signal at an antenna of a receiver device; processing,by a radio frequency front-end device, the radio frequency signal;converting, by an analog-to-digital converter, the analog signal to adigital signal; receiving, by a neural network, the digital signal; andprocessing, by the neural network, the digital signal to produce anoutput.

An exemplary embodiment of the present disclosure provides a method ofconstructing and training a neural network to process a signal. Themethod includes: identifying a processing function to be performed onthe signal by the neural network; determining, an optimum format fortraining vectors used to train the neural network; determining a numberof layers of the neural network, number of nodes per layer, the nodeconnectivity structure, and initial weights of the neural network; andinputting, into the neural network, a plurality of formatted trainingvectors in order to train the neural network to perform the processingfunction on the signal.

An exemplary embodiment of the present disclosure provides a receiverdevice configured to process a radio frequency signal. The receiverdevice includes: an antenna configured to receive the radio frequencysignal; a radio frequency front-end device configured to process theradio frequency signal; an analog-to-digital converter configured toconvert the analog signal to a digital signal; and a neural networkconfigured to receive the digital signal and to process the digitalsignal to produce an output.

BRIEF DESCRIPTION OF THE DRAWINGS

The scope of the present disclosure is best understood from thefollowing detailed description of exemplary embodiments when read inconjunction with the accompanying drawings, wherein:

FIG. 1 illustrates a system architecture in accordance with an exemplaryembodiment;

FIG. 2 illustrates a system hardware-in-the-loop architecture inaccordance with an exemplary embodiment;

FIG. 3A illustrates an end-to-end communications system architecture;

FIG. 3B is a flow chart illustrating a method according to an exemplaryembodiment;

FIG. 4 illustrates formatting an input training vector for a modulationclassifier according to an exemplary embodiment;

FIG. 5 is a flow chart illustrating a method according to an exemplaryembodiment; and

FIG. 6 is a block diagram illustrating the hardware architecture of acomputing device in accordance with an exemplary embodiment.

DETAILED DESCRIPTION

The present disclosure is directed to a wireless communication signalreceiver architecture that solves waveform interoperability problems andincreases the flexibility of radio receivers. The present disclosuredescribes a signal processing technique to enable interoperable wirelesscommunications. One or more signal processing blocks/devices in thereceiver device are replaced with one or more neural networks. Thereplacement of the classical processing block/device 310 with the neuralnetwork 312 results in a receiver device with a simplified architecturerelative to a receiver device with the classical processingblock/device. For example, a receiver device with a neural network canhave advantages in size, weight, and power (SWaP) over a conventionalreceiver. The present disclosure is also directed to a method oftraining of the neural network that is within the receiver device and/ora transmitter device.

FIG. 1 illustrates a communications system architecture in accordancewith an exemplary embodiment. The system 100 includes a transmitterdevice 102 and a receiver device 104.

In an exemplary embodiment, the receiver device 104 is configured toprocess an RF signal that is sent from the transmitter device 102. Thereceiver device 104 includes an antenna 114 that is configured toreceive the RF signal sent from the transmitter device 102. The receiverdevice 104 can include a RF front-end device 116 that is configured toprocess the RF signal, and an analog-to-digital converter 118 configuredto convert the analog RF signal to a digital signal. FIG. 1 shows thatthe RF front-end device 116 and the analog-to-digital converter 118 arelocated within the receiver device 104, but one or both of thesecomponents could be located outside of (i.e., external to) the receiverdevice 104 that contains the signal processing. The receiver device 104includes a neural network 120 that is configured to receive the digitalsignal and to process the digital signal to produce an output. That is,the receiver device 104 applies transformations to the received digitalsignal (the signal output from the analog-to-digital converter 118) torecover the bits or symbols in the transmitted signal.

The transmitter device 102 and the receiver device 104 can include amixture of neural network based and classical communications processingblocks as shown in FIG. 3A. In an exemplary embodiment, signalprocessing components including timing recovery, frequency recovery, anddemodulation have been replaced by the trained neural network 120 in thereceiver device 104 to perform the functions of these signal processingcomponents. Similarly, signal processing components including modulationand coding can be replaced by the trained neural network 106 in thetransmitter device 102. As described later, this type of architecturehas several novel applications and can enable new types of radiocommunications.

In an exemplary embodiment, the processing performed by the neuralnetwork 120 includes classifying a modulation scheme of the digitalsignal, and the digital signal is processed based on the determinedclassification of the modulation scheme. In an exemplary embodiment, theprocessing of the digital signal based on the determined classificationof the modulation scheme can be performed by a classical signalprocessing component (i.e., a non-neural network component) or multipleclassical signal processor components, or a different neural network.The modulation scheme of the digital signal can be Phase Shift Keying(PSK) modulation, Frequency Shift Keying modulation (FSK), PulseAmplitude Modulation (PAM) modulation, Gaussian Minimum Shift Keying(GMSK) modulation, Continuous Phase Modulation (CPM), QuadratureAmplitude Modulation (QAM), or any other modulation scheme. In anexemplary embodiment, the neural network 208 is able to classify any ofthe above-noted modulation schemes.

In an exemplary embodiment, the RF signal received at the antenna 114was generated by a neural network 106 in a transmitter device 102. Thetransmitter device 102 can also include a digital-to-analog converter108 that performs digital-to-analog conversion and a RF front end device110 that performs processing required after the DAC 108 and before RFtransmission, to include, for example, frequency up-conversion,filtering, amplifying, etc. The transmitter device 102 also includes anantenna 112 for transmitting the RF signal to the receiver device 104.

In an exemplary embodiment, the received RF signal is any one type amongtwo or more types of RF signals, and the classified modulation scheme ofthe digital signal is unique amongst the modulation schemes of the twoor more RF signals. That is, the neural network 208 is able to receiveone of any number of unique signal types, and classify the signal type.Under one example of a classical approach, if there are ten signaltypes, the received signal would be compared to the first signal type,then to the second signal type, then to the third signal type, and soon. Each signal type comparison requires its own unique signalprocessing operations. In contrast, in the receiver device 104 with theneural network 208 of the present disclosure, estimation of which of theten signal types is received requires fewer processing cycles through asingle common neural network.

In an exemplary embodiment, the neural network 208 in FIG. 2 is trainedto classify the digital signal. The waveform processing 202, 204, 206,is done conditionally based on the classification of the digital signalby the neural network 208.

In FIG. 1, the transmitter device 102 can be a ML-based transmitter inwhich a neural network 106 applies transformations to information bitsor symbols to generate a digital signal for transmission through thechannel (hardware+RF propagation). FIG. 1 shows the transmitter device102 with a neural network 106; however the transmitter device 102 couldbe a traditional transmitter device that does not have a neural network.

FIG. 2 illustrates an ML-based receiver with a wireless modulationscheme classifier in the receiver device 104. Subsequent waveformprocessing in the receiver device 104 is performed based on the outputof the modulation scheme classifier neural network 208. As necessary byapplication, the depth of the neural network can be extended to includeone or more additional waveform processing steps, such as,synchronization, non-linear channel correction, waveform decoding, etc.

FIG. 2 illustrates the RF test architecture for the neural network 208functioning as a modulation classifier. The system 100 of FIG. 2includes the transmitter device 102 and the receiver device 104. Thetransmitter device 102 includes a transmitter switch 200 (e.g., a switchdevice) that selects one of N waveforms (e.g., Waveform 1, Waveform 2, .. . , Waveform N) for DAC/RF processing and transmission over thechannel 304, where N can be any integer number. The neural network 208is configured to classify the received signal as one of N possiblesignals. The received signal is then routed to the appropriate waveformprocessor (e.g., Waveform 1 Processor 202, Waveform 2 Processor 204, . .. , Waveform N Processor 206) based on the classification decision madeby the neural network 208.

Applications that require processing large amounts of raw RF data atvarious degrees of fidelity benefit greatly from the signal processingtechniques of the neural network 120 in FIG. 1. One example is aspectrum sensing application where the RF front-end device 116 samplesover a wide bandwidth and is trying to separate, classify, and interpretsignals of known or unknown type in that bandwidth. The processingtechnique of the present disclosure is scalable to largecloud-processing architectures and when large amounts of computing powerare available, allows for efficient blind signal classification,separation, and interpretation. That is, in an exemplary embodiment, theneural network 120 in FIG. 1 could be located on a cloud computingenvironment instead of located on the receiver device 104.

FIG. 3A illustrates two communications system architectures. The upperarchitecture is of a classical end-to-end communications system model300, and the lower architecture is of a communications system model 306according to an exemplary embodiment of the present disclosure. Thisfigure provides a general overview of a ML-based communication system inaccordance with the present disclosure. In FIG. 3A, the transmitterdevice 102 consists of N distinct transmit processing blocks 308 ₁, 308₂, . . . , 308 _(N), each performing a distinct function to transformits input. These transmit processing blocks 308 ₁, 308 ₂, . . . , 308_(N) collectively transform the raw input bits to a digital signal fortransmission through the channel 304. The channel 304 represents theeffects of hardware and RF propagation through a transmission medium.The representing function (F(X_(N))) can vary depending on the channeltype. A receiver device 302 consists of M distinct functional receiveprocessing blocks 310 _(M), . . . , 310 ₂, 310 ₁, each performing adistinct function to transform its input. The functional receiveprocessing blocks 310 _(M), . . . , 310 ₂, 310 ₁ collectively transformthe received digital signal and recover the transmitted raw bits. Ingeneral, each receive processing block has a corresponding transmitprocessing block, with the receive processing block performing theinverse of the transmit processing block function. In FIG. 3A, M=N andthus the number of functional blocks in the transmitter device 102 andthe receiver device 302 match. However, M does not have to equal N.

The exemplary end-to-end communications system 306 shown in the lowerhalf of FIG. 3A includes the transmitter device 102, the channel 304,and the receiver device 104. In this example, one receiver block 310_(M) in the classical receiver device 302 is replaced by a neuralnetwork 312 _(M). The neural network 312 _(M) is trained to generate atits output (i.e., {circumflex over (X)}_(N-1)) the input of thecorresponding block in the transmitter (i.e., X_(N-1)). Multiple receiveprocessing blocks in the receiver 302 can be replaced by a neuralnetwork in the same fashion. The process of training the neural networkto perform its expected function in the end-to-end communications systemis described in FIG. 3B. Replacing either elements of, or the entire,receiver digital signal processing chain with a trained neural networksimplifies the communications receiver architecture.

FIG. 3B illustrates a process of training a neural network (e.g., neuralnetwork 120) for the ML-based communication system of the presentdisclosure. In step S300, the classical block(s) that is being replacedby a neural network is identified. For example, RX_(M) (block 310 _(M))for a modulation classifier in FIG. 3A. In step S302, vectors in theclassical diagram that are used for training the neural network areidentified (e.g., input=Y_(N); output=X_(N-1)). In step S304, trainingvectors are generated using classical signal processing blocks. In stepS306, the optimum format for training vectors is determined. Forexample, the format could be two-dimensional (2-D) constellation pointswith resolution dictated by the amount/type of channel distortion. StepS308 includes determining the structure of the neural network and itsinitial weights using, for example, expert knowledge. For example, atwo-layer model of the neural network can be used to identify modulationbased on a 2-D constellation input (See FIG. 4). The first layer (e.g.,Layer 1 in FIG. 4) identifies centers of mass on the constellation plotand the second layer (e.g., Layer 2 in FIG. 4) identifies the modulationbased on the combination of identified centers of mass. For example, forthe number of neurons per layer, the number of neurons in the firstlayer can be greater than the expected number of distinct centers ofmass. In an exemplary embodiment, the number of neurons in the secondlayer is equal to the number of modulations to be classified.

Step S310 includes training the neural network using formatted trainingvectors from Step S306. Step S312 includes recording the trained weightsafter completion of the training. Step S314 includes evaluating neuralnetwork performance by measuring its estimation accuracy using thetrained weights. Step S316 includes repeating steps S306 to S314 untilthe desired performance is achieved.

In an exemplary embodiment, the neural network 120 is trained on vectorsof raw or processed bits, with or without channel effects, depending onthe extent of the neural network in the transmitter device 102 andreceiver device 104. As an example, if the neural network role islimited to a modulation classifier in the receiver device 102, thetraining vector can consist of modulated data corrupted by additivewhite Gaussian noise and other distortions applicable to the desiredcommunications channel. After training, the neural network 120 canidentify an unclassified signal that has gone through a communicationschannel 304 with similar characteristics. These training vectors aregenerated by classical transmit models where information bits areredundantly encoded, modulated, and then corrupted by a channel model(e.g., F(X_(N)) in FIG. 3A).

Once properly trained, a neural network can be deployed to the edge of acommunications system into a SWaP-constrained receiver device 104. Inthis scenario, the neural network training is performed on a separateplatform than the platform onto which the neural network will bedeployed. For example, the neural network training process is performedon a system without computational constraints and with access to ampletraining data sets. The neural network is then deployed onto aSWaP-constrained receiver device for operational use. This allows for areprogrammable neural network to be deployed into a common embeddedhardware device 104. For example, a small battery-powered embedded radioreceiver running an ARM processor and a wideband RF front-end device canhost a single neural network of a given depth, width, and height. Thatis, the neural network can be trained by a cloud computing device orother computing device with a lot of processing power, and then theneural network can be stored on the receiver device 104 and/or thetransmitter device 102, which have less processing power than the devicethat trained the neural network. For example, the computing devicestoring and running the neural network 106 could be a software-definedradio (for example, an Ettus USRP e310, etc.), and the computing devicestoring and running the neural network 120 could be a software-definedradio. The receiver device 104 is software configurable subject to theperformance constraints dictated by its SWaP. Multiple neural networkscan be constructed, trained, and optimized off-platform for numerousapplications. Example applications that would require different neuralnetwork designs include signal classification, a multi-waveformreceiver, and a receiver optimized to process a single waveform in avariety of channel models. In this approach, the application-specificneural network would be deployed to the embedded device as prescribed bythe embedded device's use case.

FIG. 4 illustrates an input training vector for a neural network (e.g.,neural network 120) in a receiver device (e.g., receiver device 104)that functions as a modulation classifier. FIG. 4 shows an inputconstellation in which time domain complex samples are scaled and mappedto a 2D constellation plot 402 based on their real and imaginarycomponents. In FIG. 4, an M-by-M grid 404 is applied to theconstellation map 402. Parameter M is a design parameter. The number ofpixels (=M×M) determines the size of the input layer. In FIG. 4, thedensity of each pixel 406, 408, etc. is mapped to the corresponding node(e.g., 410 ₁, 410 ₂, . . . , 410 _(L)) in the input layer. Duringtraining of the neural network, the input layer of the neural networkholds the input training vector. In FIG. 4, Layer 1 is part of the inputlayer, and includes nodes 412 ₁, 412 ₂, . . . , 412 _(K). In FIG. 4,Layer 2 is the output layer, and includes nodes 414 ₁, 414 ₂, . . . ,414 _(N).

An exemplary embodiment of the present disclosure is directed to amethod of constructing and training a neural network 120 that isconfigured to process a signal. The method includes identifying aprocessing function (e.g., modulation classifier, timing recovery,frequency recovery, demodulation, etc.) to be performed on the RF signalby the neural network 120. The method also includes determining, anoptimum format for training vectors used to train the neural network120. For example, a training vector could be randomly generated bitsthat are rate ½ convolutionally coded, GMSK modulated, and have gonethrough an additive white Gaussian noise channel at a SNR of +10 dB. Themethod includes determining a number of layers of the neural network120, number of nodes per layer, the node connectivity structure, andinitial weights of the neural network 120. The method includesinputting, into the neural network 120, a plurality of formattedtraining vectors in order to train the neural network 120 to perform theprocessing function on the RF signal.

In an exemplary embodiment, the method can include recording trainedweights of the neural network 120 after completion of training of theneural network 120; and evaluating performance of the processingfunction of the neural network 120 by using the trained weights. Themethod can include iteratively adjusting the training vector format, thenumber of layers of the neural network 120, the number of nodes perlayer of the neural network 120, and the node connectivity structureuntil desired performance of the processing function is achieved (e.g.,a specific level of confidence is achieved in identifying a receivedsignal type).

In an exemplary embodiment, the processing function is classification ofa modulation scheme.

In an exemplary embodiment, the number of layers is two, but can be anynumber.

In an exemplary embodiment, the optimum format of the training vectorincludes two-dimensional constellation points with resolution based onan amount or type of distortion in a transmission channel 304 throughwhich the RF signal can travel.

FIG. 5 illustrates a method of processing an RF signal. The methodincludes, in step S500, receiving the RF signal at an antenna 114 of areceiver device 104. Step S502 includes processing, by a RF front-enddevice 116, the RF signal. Step S504 includes converting, by ananalog-to-digital converter 118, the analog RF signal to a digitalsignal. Step S506 includes receiving, by a neural network 120, thedigital signal. Step S508 includes processing, by the neural network120, the digital signal to produce an output.

In an exemplary embodiment, the processing can be the classifying of amodulation scheme of the digital signal, and the digital signal can beprocessed based on the determined classification of the modulationscheme.

In an exemplary embodiment, the RF signal received at the antenna 114was generated by a neural network 106 in a transmitter device 102.

In an exemplary embodiment, the received RF signal is any one type amongtwo or more types of RF signals, and the classified modulation scheme ofthe digital signal is unique amongst the modulation schemes of the twoor more RF signals.

In an exemplary embodiment, the method can include processing thedigital signal based on the determined classification of the modulationscheme.

In an exemplary embodiment, the neural network 120 is two or more neuralnetworks connected in series or parallel.

In an exemplary embodiment, the neural network 120 has been trained bytraining vectors.

In an exemplary embodiment, the neural network 120 has been trained by aplurality of training vectors that include hardware impairments anddistortions caused by a transmission channel 304 between the receiverdevice 104 and a transmitter device 102. Some radio environments, suchas under water, are extremely difficult to analytically model and haveextremely limited data sets available. For example, when transmittingthrough water, salinity, temperature, etc. affect propagation. In suchenvironments, the target channel 304 can be modeled as a neural networkthat is trained to represent the channel. In this use case, the neuralnetworks in the transmitter device 102 and receiver device 104 arejointly trained for optimum performance in the target channel 304, wherethe target channel 304 is represented by a trained neural network.During operations, the trained transmitter device 102 appliestransformations to information bits to generate a robust signal fortransmission through the channel 304. The trained receiver device 104processes the corrupt signal and recovers the transmitted informationbits with minimal errors. A signal is created that will be received thebest by the receiver device 104. That is, the signal is jointlyoptimized by the neural network 106 in the transmitter device 102 and bythe neural network 120 in the receiver device 104.

In an exemplary embodiment, the training vectors include a range oftime, phase, and frequency errors, and a range of additive whiteGaussian noise levels corresponding to a range of signal-to-noiseratios.

In an exemplary embodiment, the method can include performing, by theneural network 120, synchronization, channel equalization, demodulation,decoding, or other functions on the digital signal as necessary toreproduce information bits that were transmitted.

In an exemplary embodiment, the method can include performing, by theneural network 120, synchronization, channel equalization, demodulation,decoding, and other functions on the digital signal as necessary toreproduce information bits that were transmitted.

In an exemplary embodiment, the neural network 120 of the receiverdevice 104 and a neural network 106 of a transmitter device 102 arejointly trained for optimal performance in a particular transmissionenvironment.

FIG. 6 is a block diagram illustrating a computing device architecturein accordance with an exemplary embodiment that can be used to store andrun the neural network 120 of the receiver device of FIG. 1. A similarcomputing device architecture could be used within the transmitterdevice 102 to store and run the neural network 106. A person havingordinary skill in the art may appreciate that embodiments of thedisclosed subject matter can be practiced with various computer systemconfigurations, including multi-core multiprocessor systems,minicomputers, mainframe computers, emulated processor architectures,computers linked or clustered with distributed functions, as well aspervasive or miniature computers that may be embedded into virtually anydevice. For instance, at least one processor device and a memory may beused to implement the above described embodiments.

A hardware processor device as discussed herein may be a single hardwareprocessor, a plurality of hardware processors, or combinations thereof.Hardware processor devices may have one or more processor “cores.” Theterm “non-transitory computer readable medium” as discussed herein isused to generally refer to tangible media such as a memory device 602.The hardware processor may or may not have an RF front-end 616integrated with it—that is, the processing of collected data may occureither in the device with the antenna directly attached to it, or onanother processor device operating on previously collected signal data.

After reading this description, it will become apparent to a personskilled in the relevant art how to implement the present disclosureusing other computer systems and/or hardware architectures. Althoughoperations may be described as a sequential process, some of theoperations may in fact be performed in parallel, concurrently, and/or ina distributed environment, and with program code stored locally orremotely for access by single or multi-processor machines. In addition,in some embodiments the order of operations may be rearranged withoutdeparting from the spirit of the disclosed subject matter.

System on chip device 622 contains both the hardware processor 614 andthe hardware FPGA 610, which can be a general purpose processor deviceand a special purpose device, respectively. The hardware processordevice 614 may be connected to a communications infrastructure 612, suchas a bus, message queue, network, multi-core message-passing scheme,etc. The network may be any network suitable for performing thefunctions as disclosed herein and may include a local area network(LAN), a wide area network (WAN), a wireless network (e.g., WiFi), amobile communication network, a satellite network, the Internet, fiberoptic, coaxial cable, infrared, RF, or any combination thereof. Othersuitable network types and configurations will be apparent to personshaving skill in the relevant art. The computing device 600 may alsoinclude a memory 602 (e.g., random access memory, read-only memory,etc.), and may also include one or more additional memories. The memory602 and the one or more additional memories may be read from and/orwritten to in a well-known manner. In an embodiment, the memory 602 andthe one or more additional memories may be non-transitory computerreadable recording media. The signal processor device 608 resides insidethe hardware FPGA 610, which may perform various signal processingfunctions on the digital signal.

Data stored in the computing device 600 (e.g., in the memory 602) may bestored on any type of suitable computer readable media, such as opticalstorage (e.g., a compact disc, digital versatile disc, Blu-ray disc,etc.), magnetic tape storage (e.g., a hard disk drive), or solid-statedrive. An operating system can be stored in the memory 602.

In an exemplary embodiment, the data may be configured in any type ofsuitable database configuration, such as a relational database, astructured query language (SQL) database, a distributed database, anobject database, etc. Suitable configurations and storage types will beapparent to persons having skill in the relevant art.

The computing device 600 may also include an RF interface path 606. TheRF interface path 606 may be configured to allow software and data to betransferred between the computing device 600 and external devices.Exemplary communications interfaces 612 may include a modem, a networkinterface (e.g., an Ethernet card), a communications port, a PCMCIA slotand card, etc. Software and data transferred via the communicationsinterface 612 may be in the form of signals, which may be electronic,electromagnetic, optical, or other signals as will be apparent topersons having skill in the relevant art. The signals may travel via acommunications path, which may be configured to carry the signals andmay be implemented using wire, cable, fiber optics, a phone line, acellular phone link, a radio frequency link, etc. The timing interfacepath 620 or the debug interface path 618 may be used to configure thehardware FPGA 610 to optimize the signal processor 608.

Memory semiconductors (e.g., DRAMs, etc.) may be means for providingsoftware to the computing device 600. Computer programs (e.g., computercontrol logic) may be stored in the memory 602. Computer programs mayalso be received via the communications interface 612. Such computerprograms, when executed, may enable computing device 600 to implementthe present methods as discussed herein. In particular, the computerprograms stored on a non-transitory computer-readable medium, whenexecuted, may enable hardware processor device 602 to implement thefunctions/methods illustrated by FIGS. 2, 3A, 3B, 4, and 5, or similarmethods, as discussed herein. Accordingly, such computer programs mayrepresent controllers of the computing device 600. Where the presentdisclosure is implemented using software, the software may be stored ina computer program product or non-transitory computer readable mediumand loaded into the computing device 600 using a removable storage driveor communications interface 612.

The computing device 600 may also include a transceiver which performsfunctions pertaining to analog to digital signal conversion. Thecomputing device 600 may also include an RF front end 616 which performsRF signal processing functions on an RF signal. The computing device 600may also contain a power device 604 which powers the device to performits designated functions.

Thus, it will be appreciated by those skilled in the art that thedisclosed systems and methods can be embodied in other specific formswithout departing from the spirit or essential characteristics thereof.The presently disclosed embodiments are therefore considered in allrespects to be illustrative and not restricted. It is not exhaustive anddoes not limit the disclosure to the precise form disclosed.Modifications and variations are possible in light of the aboveteachings or may be acquired from practicing of the disclosure, withoutdeparting from the breadth or scope. Reference to an element in thesingular is not intended to mean “one and only one” unless explicitly sostated, but rather “one or more.” Moreover, where a phrase similar to“at least one of A, B, or C” is used in the claims, it is intended thatthe phrase be interpreted to mean that A alone may be present in anembodiment, B alone may be present in an embodiment, C alone may bepresent in an embodiment, or that any combination of the elements A, Band C may be present in a single embodiment; for example, A and B, A andC, B and C, or A and B and C.

No claim element herein is to be construed under the provisions of 35U.S.C. 112(f) unless the element is expressly recited using the phrase“means for.” As used herein, the terms “comprises,” “comprising,” or anyother variation thereof, are intended to cover a non-exclusiveinclusion, such that a process, method, article, or apparatus thatcomprises a list of elements does not include only those elements butmay include other elements not expressly listed or inherent to suchprocess, method, article, or apparatus. The scope of the invention isindicated by the appended claims rather than the foregoing descriptionand all changes that come within the meaning and range and equivalencethereof are intended to be embraced therein.

1-12. (canceled)
 1. A method of constructing and training a neuralnetwork that is configured to process a signal, the method comprising:identifying a processing function to be performed on the signal by theneural network; determining, an optimum format for training vectors tobe applied to the neural network; determining a number of layers of theneural network, number of nodes per layer, the node connectivitystructure, and initial weights of the neural network; and inputting,into the neural network, a plurality of formatted training vectors inorder to train the neural network to perform the processing function onthe signal.
 2. The method of claim 13, comprising: recording trainedweights of the neural network after completion of training of the neuralnetwork; evaluating performance of the processing function of the neuralnetwork by using the trained weights; and iteratively adjusting thetraining vector format, the number of layers of the neural network, thenumber of nodes per layer of the neural network, and the nodeconnectivity structure until desired performance of the processingfunction is achieved.
 3. The method of claim 13, wherein the processingfunction is classification of a modulation scheme.
 4. The method ofclaim 13, wherein the number of layers is two.
 5. The method of claim13, wherein the optimum format of the training vector includestwo-dimensional constellation points with resolution based on an amountor type of distortion in a transmission channel through which the radiofrequency signal can travel. 18-22. (canceled)